The subject matter discussed in the background section should not be assumed to be prior art merely as a result of its mention in the background section. Similarly, a problem mentioned in the background section or associated with the subject matter of the background section should not be assumed to have been previously recognized in the prior art. The subject matter in the background section merely represents different approaches, which in and of themselves may also be inventions.
Subsurface hydrocarbon reservoirs may represent 100's of millions to many billions of dollars of fluid, such as oil and natural gas. Due to this value, it is important to characterize petrochemical fluid dynamics to the greatest degree possible, which will help understand the present and future value of the reservoir and how to optimize management of related oil and gas fields accessing these subsurface hydrocarbon reservoirs.
One way to model a subsurface hydrocarbon reservoir is to define a set of ordinary and partial differential equations modeling petrochemical fluid dynamics. There is a field of endeavor for defining and solving these equations in a host space using an artificial neural network. Unfortunately, these networks have limitations when the host space includes one or more discontinuities.
While techniques to model solutions of partial differential equations with neural networks have been recently developed, robust approaches to handle Neumann boundary conditions do not exist. It is critical to handle such boundary conditions to model no flow boundaries in reservoir simulation such as faults and pinch-outs. Such boundaries create discontinuities in the states of the system, thereby making it difficult to represent with smooth functions such as neural networks. Non-neighborhood connection (NNC) approach has been generally accepted as the solution to solve this problem for reservoir simulation based on finite volume meshes. However, such approaches are not applicable to meshless methods as above are the concept of connections is not defined.
When the host space represents a subsurface hydrocarbon reservoir, there may be physical discontinuities. For example, some of the applicable partial differential equations may relate to fluid flow in the reservoir. Within the reservoir, there may be physical structures that wholly or partially block fluid flow at various locations. While a position and orientation of these physical structures may be known or estimated from seismic data, a straightforward application of a neural network will fail at boundaries of these physical structures.
It may be advantageous to provide a system or method for characterizing subsurface hydrocarbon reservoirs, such as through fault modeling in low order continuous scale simulation of real world subsurface hydrocarbon reservoirs having discontinuities and improving an accuracy and speed of the characterizations.